KCEP2105 Numerical Methods & Statistics Dr Liew HL

Homework 5

Out 21 May, Due 30 May (due in class) Grading (#-pts): 1-40, 2-20, 3-20, 4-20, 5-20. (Total: 120) 1. The following tables are the data for particulate matter (PM) emissions (in g/gal) for 62

vehicles driven at high altitude. The notation 1-

KCEP2105 Numerical Methods & Statistics Dr Liew HL

2. A process that manufactures piston rings produces ring whose diameter (in cm) vary according to the probability density function:

31 16 109.75 10.25

0otherwise.

a. What proportion of piston rings have diameter less than 9.5 cm? b. The spec is 10.0 0.1cm. What proportion is within spec?

3. Calculate: (a) mean, (b) variance, and (c) median (50-percentile) for the probability function in Problem 2.

4. Fill in all blanks. Submit your work by writing out everything in full and underlining the blank parts.

KCEP2105 Numerical Methods & Statistics Dr Liew HL

5. Shafts manufactured for use in optical storage devices have diameters that are normally distributed with mean 0.652 cm and standard deviation 0.003 cm. The specification for the shaft diameter is 0.650 0.005cm.

a. What proportion of the shaft manufactured by this process meet the specification? b. The process can be adjusted through calibration. If the mean is set to 0.650 cm,

what proportion of shafts will meet specification? c. If the mean is set to 0.650 cm and 99% of the shafts meet the specification, what

is the SD?